Method for determining distances in the anterior ocular segment

ABSTRACT

The invention relates to a method for determining distances in the anterior ocular segment, preferably of the pupils and/or the diameter of the iris, wherein the image of at least part of the eye is recorded and digitized using an imaging device and an array for illuminating the eye. On the basis of said digital image, a center of gravity analysis and the determination of the central point are carried out, especially for the position of the pupils, by conducting an intensity and threshold analysis as rough determination. Based on said rough determination, a fine detection of the position of the edges of the pupil and/or the edges of the iris is carried out. Additionally, the angle between the visual axis and the optical axis of the eye can be determined from the position of a fixed reflection to the center of the pupil and/or the center of the iris.

The IOL (intraocular lens) calculation formula “Holladay 2”(“Intraocular Lens Power Calculations for the Refractive Surgeon”, JackT. Holladay, in: Operative Techniques in Cataract and RefractiveSurgery, Vol. 1, No. 3 (September), 1998: pp 105-117), by which thepower of an intraocular lens (IOL) for implantation into the human eyecan be calculated, as well as the selection of special types of IOL (ICLetc.), require the so-called “horizontal white-to-white distance”(hor-w-t-w), which is the horizontal diameter of the iris, as an inputvalue.

In corneal surgery for the removal of visual deficiciencies in the humaneye (PRK, LASIK), it is also interesting for the surgeon to know atwhich point the patient's visual axis passes through the cornea.Thereafter, laser ablation can be effected more precisely at this pointthan according to the previous assumption based on the geometric centerof the cornea.

The interferometric length measurement of the thickness of the cornea,of the anterior chamber depth and of the lens thickness in the human eyeusing PCI requires preadjustment of the eye along its theoreticaloptical axis in front of the measurement instrument, as opposed to theaxial length measurement which requires positioning of the eye along theactual visual axis.

In order to determine the “hor-w-t-w”, use was previously made of rulersand templates (FIG. 11, which are held in front of the patient's eye andfrom which the diameter of the iris is thus read by taking a fix. Thismethod is susceptible to interference by parallax during observation,and the templates previously used have a 0.5 mm grading, allowing onlylimited precision. Another known solution are measuring eyepiecesemployed as fittings on slit lamp devices (Instruction Manual forslit-lamp 30 SL/M, publication no.: G 30-114-d (MAX1/79) Carl ZeissD-7082 Oberkochen, page 38). Although such eyepieces prevent parallaxerrors, the diameter value has to be read from a scale.

Further, invasive measurement means are known in the form of mechanicalslide gauges which are inserted into the anterior chamber through anincision in the sclera (e.g. U.S. Pat. No. 4,319,564).

Further, gonioscopes, as they are called, are known which are placed onthe eye, project scales onto the iris and allow the iris diameter to beread through magnifying glasses (e.g. U.S. Pat. No. 4,398,812).

Devices which measure the diameter of the pupil are referred to aspupillometers (e.g. EP 0,550,673). However, they do not measure thediameter of the iris.

No devices are known for determining the point where the visual axispasses through the cornea. The camera industry merely uses methods whichdetect the direction in which a human eye is looking; the output signalsof such arrangements serve, for example, to control autofocus mechanismsin photographic cameras (e.g. U.S. Pat. No. 5,291,234), or they are usedin so-called eye trackers. Said devices monitor eye movements or viewingmovements.

Also, no devices are known for preadjustment of the eye along theoptical axis; by focusing the eye differently or by scanning themeasuring beam, rather haphazard efforts are made to find the rightpositioning of the eye along the optical axis by trial.

The applicant's WO 00/33729 discloses a system and a method fordetermining, in a non-contacting manner, the axial length, the corneacurvature and the anterior chamber depth of the eye using one singledevice to calculate the optical effect of an intraocular lens. The eyeis generally illuminated via visible or IR LEDs, the reflection imagesthereof being captured by the CCD camera and displayed. Further, afixation light is provided for the test subject to direct the pupil ofthe eye in the direction of the optical axis, the reflection of thefixation light also being captured by the CCD camera.

It is an object of the invention to provide a device and a methodallowing higher precision of the hor-w-t-w determination in auser-independent manner. According to the invention, this object isachieved by the features of the independent claims. Preferred furtherembodiments are the subject of the dependent claims.

In a surprising manner, the invention also realizes a practicalpossibility of describing the point of intersection of the visual axisthrough the cornea relative to the center of the pupil and/or the centerof the iris and of enabling a more precise preadjustment of aninterferometric length measurement instrument along the optical axis ofthe eye, based on the position of said intersection point and on thegeometric center of the cornea.

The position of the visual axis was previously unknown to the user ofsuch instrument. Therefore, the patient was requested to focusdifferently by suitable means (fixation light for the patient's eyewithin the instrument or outside the instrument). Thereupon, ameasurement operation was initiated, which was only successful if themeasurement was effected along the optical axis. This means that it isnot clear whether or not this axis has been hit until after saidmeasurement operation.

The fixation light is moved in increments of 1°; quite a few uselessmeasurement operations may be required until the point is reached wheresaid interferometric measurement is successful.

Such procedure is not acceptable in the ophthalmological routine.

Embodiment example:

The invention is described in greater detail below with reference to theschematic drawings, wherein:

FIG. 1 is a flowchart of the method according to the invention,

FIG. 2 shows the algorithm for rough detection of the pupil,

FIG. 3 represents the gray scale analysis/center determination,

FIG. 4 represents the edge analysis,

FIG. 5 is a flowchart of the edge analysis,

FIG. 6 shows the detection and determination of the fixation pointposition,

FIG. 7 is a flowchart of the plausibility check,

FIG. 8 shows the illumination beam path/detection beam path,

FIG. 9 is an overview over the eye to be measured,

FIG. 10 is an enlarged view of the center of FIG. 9,

FIG. 11 shows a white-to-white gauge according to Holladay-Godwin.

According to FIG. 8, the eye 1 of the test subject is illuminated bypreferably infrared-light emitting light sources 2, which are arrangedin a circle around the optical axis, as in WO 00/33729 (e.g. LED). Alight source 3, onto which the test subject focuses, is faded in at theobservation system, coaxially to the observation beam path, by a beamsplitter 4, said light source 3 emitting visible light (e.g. LED orlaser diode).

The image of the eye is imaged, via a telecentric imaging system 5 ontoan image sensor 6, preferably a CCD camera, which is connected to acontrol and evaluation unit (not shown). The video signal of the camerais displayed on a screen or LC display (not shown).

The illumination 2 allows the user, during the entire time of adjustmentand of measurement of the test subject, to check whether the testsubject is focusing correctly—and, consequently, whether the result ofsaid measurement is correct. The imaging of the test subject's eye withthe relevant image details is effected in a telecentric manner so as tominimize the influence of the adjustment of the test subject.

Upon correct adjustment of the patient's eye and upon initiation by theuser, the BAS signal of the CCD camera is taken over into the memory ofa computer via a frame grabber. FIG. 9 schematically shows such image,including pupil 7, pupil diameter 9, as well as iris 8 and iris diameter10. FIG. 10 shows an enlarged segment of the pupil with reflectionpoints 11 of the illumination, the image of the fixation light 12, theiris center 13 and the pupil center 14.

Using means of image processing, the distances within said image aredetermined, from which the following values can be calculated on thebasis of the image scale of the observation optics:

-   -   the diameter and the center of the iris,    -   the diameter and the center of the pupil,    -   the x and y coordinates of the cornea image of the fixation        light (1^(st) Purkinje image) relative to the center of the        iris, and    -   the x and y coordinates of the cornea image of the fixation        light (1^(st) Purkinje image) relative to the center of the        pupil.

Since the real shapes of the iris and pupil of the human eye do notnecessarily have to be circles, ellipses with their parameters ofsemiaxes and focal points may be determined as well, according to afurther embodiment.

With a suitably selected image scale of the imaging optics 5, themeasured values can be determined with a computational precision of<±0.01 mm.

The diameter of the iris yields the horizontal white-to-white distance:

-   white-to-white [in mm]=∘_(iris) [in pixels]/number of pixels per mm.

The x and y coordinates of the Purkinje image of the fixation lightyield the point where the visual axis passes through the cornea,provided that the test subject is focusing correctly, which the user cancheck during measurement on the basis of the live video image on the LCdisplay. The visual axis and optical axis may deviate from each other byup to 8°, because the fovea may be offset from 3° nasally to 8°temporally. (Simplified schematic eye according to Gullstrand in Diepes“Refraktionsbestimmung” Bode publishing company, Pfortzheim, 5^(th)edition 1988).

The angle between the visual axis and the optical axis of the eyeresults from angular relationships, for example, on the basis of theGullstrand eye, wherein the measured offset (distance) between the imageof the fixation point and the iris center and/or the pupil center istaken into account.

Prior to the interferometric measurement of the anterior ocular media,the deviation of both visual axes from one another is determined.

The fixation point of the present measurement system is marked along thevisual axis. The amount and the direction of the distance of this pointto the center of the pupil (and/or the center of the iris) isdetermined.

Simple trigonometric formulae yield the required angle between theoptical axis and the visual axis, for example, as:

-   α=arc tan (a/k)-   α—angle between visual axis and optical axis-   α—distance between fixation point and pupil center (iris center)-   k—distance between nodal point (see Diepes reference) and cornea    minus R/2 (approximately 3.8 mm).

According to this measured value, a preadjustment of the patient'sviewing direction may advantageously be effected by providing a fixationlight to the patient at the calculated angle α, thus obviating a complexsearch procedure.

Method for Determining the Positions of Pupil, Iris and Fixation Point

Flowchart (FIG. 1):

As input value for evaluation, a digitized gray scale image is used atan image scale allowing the entire iris to be captured with turned-onsurround field illumination.

After noise reduction, the evaluation unit determines the objects:pupil, iris and fixation point image.

Advantageously, the pupil image is roughly determined at first and usedfor iris detection, since the contrast at the iris edge is usually weakand, moreover, the iris periphery may be covered by the eye lids at thetop and bottom thereof, so that no circular, but only sector-shapedsensing is possible.

Upon successful execution, the parameters of the iris and of the pupilare returned as a circular model (radius, center) or as an ellipticmodel (main axes, center). The fixation point (i.e. the point where thevisual axis passes through the cornea) is returned in the form of itscoordinates, i.e. the coordinates are available to the calling program.

Noise Reduction

Edge detection on the basis of gray scale profiles in the original imageleads to great variations in determining the edge locations, saidvariations resulting from noise superpositioned on the image signal. A20×20 median filter is used for noise reduction.

Rough Detection of the Pupil—FIG. 2/FIG. 3

For rough detection of the position of the pupil, a binarization methodwith subsequent search for joined objects in the binary image is used.

FIG. 3 shows an uneven gray scale distribution g (x,y), sensed by theCCD camera and determined by threshold value analysis (threshold value1), in an X/Y coordinate system. The theoretical center xo,yo of thisarea is determined by a centroid analysis, and a circularmodel/elliptical model having a radius R is determined. (This will beexplained hereinafter).

Binarization refers to the pixel-wise gray scale transformationaccording to

${b\left( {x,y} \right)} = \left\{ {\begin{matrix}1 & {{{if}\mspace{14mu}{g\left( {x,y} \right)}} \geq {thr}} \\0 & {otherwise}\end{matrix},} \right.$wherein

x horizontal coordinate of a pixel y vertical coordinate of a pixel g(x, y) gray scale value of the pixel at the location (x, y) thrnon-negative threshold value

The pupil is assumed to be that binary object which exceeds apredetermined minimum and is closest to the image center. Due to itsdependence on ambient brightness, a binarization method with a constantthreshold value is not suitable. Therefore, binary objects aredetermined for a series of threshold values according to the abovemethod. The “optimum” threshold value thr* is assumed to be that valuewhich, upon being incremented, results in the smallest change in theselected binary object (i.e. position and size). On the basis of thebinary object allocated to this threshold value, the following factorsare determined for a rough assessment of the position of the pupil:

$x_{0} = \frac{\sum\;{{g\left( {x,y} \right)} \cdot x}}{\sum\;{g\left( {x,y} \right)}}\mspace{14mu}\left( {{Summation}\mspace{14mu}{over}\mspace{14mu}{all}\mspace{14mu}{pixels}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{image}} \right)$$y_{0} = \frac{\sum\;{{g\left( {x,y} \right)} \cdot y}}{\sum\;{g\left( {x,y} \right)}}$$R = {\sqrt{\frac{1}{\pi}{\sum\;{g\left( {x,y} \right)}}}\mspace{14mu}{with}}$$\;{{g\left( {x,y} \right)} = \left\{ \begin{matrix}{1\left( {x,y} \right)} & {\in {{binary}\mspace{14mu}{object}}} \\\; & {0\mspace{14mu}{otherwise}}\end{matrix} \right.}$

(x₀, y₀) centroid of the binary object (center coordinates) R (area ofthe binary object/π)^(1/2) (estimated radius).Fine Detection of Pupil and Iris—FIG. 4

The edge locations for the pupil and iris (edge=“periphery” of thecircle/ellipse) are determined from gray scale profiles (=scans of thegray scale values of the median-filtered image along paths) via thecenter of the roughly determined pupil (see Figure). For the iris, it isassumed, first of all, that the edge is located in a specific, largercircular ring, arranged concentrically to the roughly detected pupil.The following algorithm applies analogously to the fine detection ofboth the pupil edge and the iris edge.

Scanning was effected by means of search beams (search directions) Sstarting from xo,yo, with the search beam direction being successivelyvaried by an angle α. The rough search range SB on the search beam S isobtained from the already determined rough model of iris and pupil. Thedetermination of the pupil edge K is effected over the entire circle,while the iris edge determination only takes place in an angular regionaround the X axis (2 sectors of a circle) due to possible lid covering.

In these profiles, turning points are determined by suitable smoothingand numerical differentiation. A number of methods are known for thispurpose (e.g. Savitzky A. and Golay, M. J. E. Analytical Chemistry, Vol.36, pp. 1627-39, 1964), which may be efficiently implemented asone-dimensional, linear filters. In general, a multiplicity of turningpoints will be found along the gray scale profile. Among these, thatposition (x,y) which meets the following conditions is determined as anedge location:

-   -   (a) (x,y) is located in a circular ring around (x₀,y₀) (rough        position of the pupil) having an internal radius and an external        radius, which may be individually determined for the pupil        detection and the iris detection, respectively, as a function of        r0 (rough radius of the pupil).    -   (b) The difference, in absolute terms, between the extreme        values located around (x,y) in the gray scale profile reaches        its maximum at all positions that meet (a).

Thus, a maximum of two edge locations each are available per gray scaleprofile (i.e. per scanning angle α) for iris modelling and for pupilmodelling, respectively. In order to eliminate systematic interferences,for example, caused by the iris or the pupil being covered in the caseof a narrow eyelid opening, the range of scanning angles used may berestricted, i.e. α_(min, iris)<α<α_(max, iris) for iris edgedetermination and, analogously, α_(min, pupil)<α<α_(max, pupil) forpupil edge determination.

Adaptation of the Pupil/Iris Model—FIG. 5

The number of edge locations (xi, yi) determined in the preceding stepallows the parameters of the pupil model and of the iris model (i.e.either circle or ellipse) to be determined by means of regression. Thisis done by minimizing the sum of square errors

$\begin{matrix}\left. {{\sum\limits_{i}\left( {x_{i} - {x\left( {x_{i},y_{i},p} \right)}} \right)^{2}} + \left( {y_{i} - {y\left( {x_{i},y_{i},p} \right)}} \right)^{2}}\rightarrow\min \right. & (1)\end{matrix}$over the number of possible parameter vectors p (circle: centercoordinates and radius; ellipse: center coordinates, lengths of the mainaxes, angle(s) between the great main axis and the x axis). Foradjustment of the circle, a solution of (1) is possible in a direct andnumerically efficient manner by the method of singular valuedistribution. For the solution of the restricted root-mean-square valueproblem for adaptation of the ellipse, there also exist a number ofstandard approaches (e.g. in Bookstein, F. L. Fitting conic sections toscattered data. Computer Graphics and Image Processing, Vol. 9, pp.56-71, 1979, and Fitzgibbon, A. W. and Fisher, R. B. A buyer's guide toconic fitting. Proceedings of British Machine Vision Conference,Birmingham, 1995).

In order to reduce the influence of wild values (i.e. incorrectlydetermined edge locations), use is made of a two-step regression methodaccording to FIG. 5.

Moreover, alternative methods for selection of the edge locations whichare to be used for parameter adaptation can be used, such as the Houghtransformation for circular models.

Detection of the Fixation Point—FIG. 6

For detection of the fixation point, a binarization (see above) of theunfiltered image of the CCD camera is effected with a threshold valueΘ_(FP)=s*thr* (s>1.0), said threshold value depending on thr* (thresholdvalue used for the rough detection of the pupil). As the fixation point,there is determined the center of that integral binary object BF (grayscale values >Θ_(FP)) which is located closest to the determined pupilcenter PM and has a predetermined minimum surface area.

Other, non-relevant binary objects (e.g. reflection images of the LEDillumination) are identified through their greater distance from thepupil center and are not taken into consideration.

Plausibility Check—FIG. 7

Before the determined coordinates are returned to the calling program, aplausibility check according to FIG. 7 is effected in order to preventthat possibly incorrectly detected elements are found. Interrogationscomprise previously known properties of the examined object, with whichthe determined results must be coincident.

1. A method for measuring a pupil diameter and/or an iris diameter,comprising of: capturing an image of at least part of the eye with animage capture unit and an illumination system; digitizing the capturedimage; determining rough values of a pupil center and a radius of thepupil via an intensity threshold analysis; and performing a finedetection of edges of the pupil and/or an iris on the basis of the roughdetermination wherein the fine detection comprises scanning thedigitized captured image along linear paths generally crossing theroughly detected pupil center wherein edges are detected along thelinear paths and wherein the linear paths are within a limited angularregion around a horizontal axis of the pupil; and modeling the iris andthe pupil by using a generally circular or a generally elliptic model ofthe edges of the iris and the pupil.
 2. The method as claimed in claim1, in which the structure whose edges are finely detected is selectedfrom a group consisting of the pupil and the iris.
 3. The method asclaimed in claim 1, further comprising the step of determining anintersection point of a visual axis of the eye with a cornea by the useof a fixation light.
 4. The method as claimed in claim 1, furthercomprising the step of determining an intersection point of a visualaxis with the cornea with relation to the pupil or the iris on the basisof a position of a fixation reflection.
 5. The method as claimed inclaim 1, further comprising the step of determining an angle between avisual axis of the eye and an optical axis of the eye based on aposition of a fixation reflection relative to a center of the pupil or acenter of the iris.
 6. The method as claimed in claim 5, furthercomprising the step of preadjusting an instrument for interferometricmeasurement of the segments of the eye along the optical axis of the eyeusing the angle determined.
 7. A device for measuring a pupil diameterand/or an iris diameter, comprising: an image capture unit to capture animage of at least a portion of the eye; an illumination system toilluminate the eye to facilitate the image capture; a digitizer todigitize the captured image; a microprocessor; and software adapted todirect the microprocessor to determine rough values of a pupil centerand a radius of the pupil; and subsequently, a fine detection analysisto determine the position of the edges of the structure based on therough location wherein the fine detection comprises: scanning thedigitized captured image alone linear paths generally crossing theroughly detected pupil center wherein edges are detected along thelinear paths and wherein the linear paths are within a limited angularregion around a horizontal axis of the pupil; and modeling the iris andthe pupil by using a generally circular or a generally elliptic model ofthe edges of the iris and the pupil.
 8. The device as claimed in claim7, in which the structure of whose edges are finely detected is selectedfrom a group consisting of the pupil and the iris.
 9. The device asclaimed in claim 7, further comprising software to direct themicroprocessor to determine an intersection point of a visual axis withthe cornea by the use of a fixation light.
 10. The device as claimed inclaim 7, further comprising software to direct the microprocessor todetermine an intersection point of a visual axis with the cornea withrelation to the pupil or the iris on the basis of a position of afixation reflection.
 11. The device as claimed in claim 7, furthercomprising software to direct the microprocessor to determine an anglebetween a visual axis of the eye and an optical axis of the eye based ona position of a fixation reflection relative to a center of the pupil ora center of the iris.
 12. The device as claimed in claim 11, furthercomprising software to direct the microprocessor to preadjust aninstrument for interferometric measurement of the segments of the eyealong the optical axis of the eye using the angle determined.
 13. Adevice for measuring a pupil diameter and/or an iris diameter,comprising: means for capturing an image of at least part of the eye;means for illuminating the eye; means for digitizing the captured image;means for performing rough values of a pupil center and a radius of thepupil via an intensity threshold analysis; and means for performing afine detection of edges of the structure on the basis of the roughdetermination wherein the fine detection comprises: scanning thedigitized captured image along linear paths generally crossing theroughly detected pupil center wherein edges are detected along thelinear paths and wherein the linear paths are within a limited angularregion around a horizontal axis of the pupil; and modeling the iris andthe pupil by using generally circular or a generally elliptic model ofthe edges of the iris and the pupil.
 14. The device as claimed in claim13, in which the structure whose edges are finely detected is selectedfrom a group consisting of the pupil and the iris.
 15. The device asclaimed in claim 13, further comprising means for determining anintersection point of a visual axis with the cornea by the use of afixation light.
 16. The device as claimed in claim 13, furthercomprising means for determining an intersection point of a visual axiswith the cornea with relation to the pupil or the iris on the basis of aposition of a fixation reflection.
 17. The device as claimed in claim13, further comprising means for determining an angle between a visualaxis of the eye and an optical axis of the eye based on a position of afixation reflection relative to a center of the pupil or a center of theiris.
 18. The device as claimed in claim 17, further comprising meansfor preadjusting an instrument for interferometric measurement of thesegments of the eye along the optical axis of the eye using the angledetermined.